33. Electric potential is a ______________ quantity
A. Vector
B. Scalar
C. Tensor
D. Pseudo Vector
Electric Potential: Scalar or Vector?
Option Analysis
- A. Vector: Vectors possess both magnitude and direction, such as the electric field defined by 𝐄 = −∇V. However, the electric potential de>V lacks direction and combines algebraically, not vectorially. Therefore, it is not a vector quantity.
- B. Scalar: Correct. Electric potential is defined as the work done per unit charge:
de>V = (1 / 4πϵ₀) · (Q / r)
It depends only on scalar quantities—charge magnitude de>Q and distance de>r. Potentials superpose by simple addition, reinforcing their scalar nature. - C. Tensor: Tensors generalize scalars and vectors, transforming according to coordinate systems and indices (e.g., stress tensor). Electric potential is a rank‑0 tensor, meaning it is a scalar and not a higher‑order tensor.
- D. Pseudo Vector: Pseudovectors (or axial vectors), such as the magnetic field de>𝐁, reverse sign under parity inversion but behave like vectors otherwise. The electric potential remains unchanged under inversion, confirming it as a true scalar.
Key Concepts
The electric potential arises from a conservative electric field—its line integral depends only on the endpoints. The gradient of potential yields the electric field vector, but the potential itself is a scalar quantity, ensuring path independence.
This distinction between scalar potential and vector field is crucial in electromagnetism and often forms the basis for conceptual questions in competitive exams like CSIR NET and GATE Physics.
